Basic proportionality theorem
Imagine you have a big cake and you want to cut it into equal pieces. If the cake is cut straight down the middle, each piece will be the same size. However, what if you want to cut the cake into 3 pieces?
Here's where the basic proportionality theorem comes in.
If you want to cut the cake into 3 pieces that are equal in size, you need to cut the cake into 4 slices (pieces).
Why 4 slices? Because if you cut the cake into 4 equal slices and take away one slice, the remaining 3 slices are still equal in size.
Basically, the basic proportionality theorem says that if you have two or more similar shapes, and you draw a line that cuts through those shapes, the parts of those shapes on each side of the line are proportional (meaning they have the same ratio).
In our cake example, the line we drew was the cut we made to create the slices. The parts of the cake on each side of the cut (the slices) are proportional because they are all equal in size.
This theorem is useful in many different fields, from cooking to math to engineering, because it helps us understand how parts of similar shapes relate to each other.
Here's where the basic proportionality theorem comes in.
If you want to cut the cake into 3 pieces that are equal in size, you need to cut the cake into 4 slices (pieces).
Why 4 slices? Because if you cut the cake into 4 equal slices and take away one slice, the remaining 3 slices are still equal in size.
Basically, the basic proportionality theorem says that if you have two or more similar shapes, and you draw a line that cuts through those shapes, the parts of those shapes on each side of the line are proportional (meaning they have the same ratio).
In our cake example, the line we drew was the cut we made to create the slices. The parts of the cake on each side of the cut (the slices) are proportional because they are all equal in size.
This theorem is useful in many different fields, from cooking to math to engineering, because it helps us understand how parts of similar shapes relate to each other.